Question

Write the equation of the line in standard form

1.) The line is parallel to the graph of 2x-3y=-3 and with the y-intercept=6.​

Answer 1

2x - 3y = 18

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x - 3y = - 3 into this form by subtracting 2x from both sides

- 3y = - 2x - 3 ( divide all terms by - 3 )

y =
`(2)/(3)` x + 1 ← in slope- intercept form

with slope m =
`(2)/(3)`

Parallel lines have equal slopes, thus

y =
`(2)/(3)` x + c ← is the partial equation

Given the y- intercept = 6, then

y =
`(2)/(3)` x + 6 ← equation in slope- intercept form

Multiply through by 3

3y = 2x + 18 ( subtract 3y from both sides )

0 = 2x - 3y + 18 ( subtract 18 from both sides )

2x - 3y = - 18 ← equation in standard form